In this section we give a short algorithm that allows us to convert bounded real-valued Borel flows into bounded integral Borel flows, assuming that the graph admits a connected toast. This is applicable to finding Borel equidecompositions. Namely, as shown by Marks and Unger in [1]}, the existence of bounded integral Borel flows can be used to prove equidecomposition results using tilings such as the Gao–Jackson tilings [2]} for actions of \(\mathbb {Z}^d\) . In the next section we will use these ideas to prove our results on measurable equidecompositions.
